Multibranch Elastic Bound States in the Continuum

Shuowei An, Tuo Liu, Liyun Cao, Zhongming Gu, Haiyan Fan, Yi Zeng, Li Cheng, Jie Zhu, and Badreddine Assouar

Phys. Rev. Lett. 132, 187202 – Published 30 April 2024

Abstract

Constructing a highly localized wave field by means of bound states in the continuum (BICs) promotes enhanced wave-matter interaction and offers approaches to high-sensitivity devices. Elastic waves can carry complex polarizations and thus differ from electromagnetic waves and other scalar mechanical waves in the formation of BICs, which is yet to be fully explored and exploited. Here, we report the investigation of local resonance modes supported by a Lamb waveguide side-branched with two pairs of resonant pillars and show the emergence of two groups of elastic BICs with different polarizations or symmetries. Particularly, the two groups of BICs exhibit distinct responses to external perturbations, based on which a label-free sensing scheme with enhanced-sensitivity is proposed. Our study reveals the rich properties of BICs arising from the complex wave dynamics in elastic media and demonstrates their unique functionality for sensing and detection.

Received 12 December 2022
Accepted 1 April 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.187202

Physics Subject Headings (PhySH)

Acoustic metamaterials Acoustics Bound states in the continuum

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Shuowei An ^1,*, Tuo Liu ^2,3,*, Liyun Cao ^4,*, Zhongming Gu⁵, Haiyan Fan ¹, Yi Zeng ⁴, Li Cheng ^1,†, Jie Zhu^5,‡, and Badreddine Assouar ^4,§

¹Department of Mechanical Engineering, Hong Kong Polytechnic University, Hong Kong, China
²Key Laboratory of Noise and Vibration Research, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China
³State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China
⁴Université de Lorraine, CNRS, Institut Jean Lamour, Nancy 54000, France
⁵Institute of Acoustics, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China

^*These authors contributed equally to this work.
^†Corresponding author: li.cheng@polyu.edu.hk
^‡Corresponding author: jiezhu@tongji.edu.cn
^§Corresponding author: badreddine.assouar@univ-lorraine.fr

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Issue

Vol. 132, Iss. 18 — 3 May 2024

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Images

Figure 1
Lamb waveguide with two pairs of side-branched resonators. (a) Schematic of the pillared elastic waveguide. It supports both extensional (red dashed line) and flexural waves (black solid line). (b) Model representation of the four resonators ( $R_{1}$ , $R_{2}$ , $R_{3}$ and $R_{4}$ ) coupled via the bus waveguide. For simplicity, only the couplings of $R_{1}$ with other pillars are plotted.
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Figure 2
BICs and quasi-BICs in pillared elastic waveguide. (a) Resonance frequencies [the real part of eigenfrequency, $Re (f_{eig})$ ] and $Q$ factors of the antisymmetric and symmetric branches of eigenmodes as a function of $d$ . The color scale represents the amplitude of $Q$ in decibels (dB). (b) Mode shapes of the corresponding BICs and quasi-BICs. $u$ and $v$ are horizontal ( $x$ ) and vertical ( $y$ ) displacement components. (c) Measured frequency response and field distributions for the local modes in branch $A_{0}^{'}$ and $S_{1}^{'}$ . Left panel: frequency response functions (FRFs) of vertical velocity component $| \dot{v} |$ . The dotted lines trace the peaks of $S_{1}^{'}$ and $A_{0}^{'}$ . Upper right panel: photo of the sample and experimental setup. Lower right panel: field distributions of $| \dot{v} |$ at the peaks I–V marked in the left panel (see animations of fields in [53]).
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Figure 3
Variations of the antisymmetric BIC in $A_{1}$ and symmetric quasi-BIC in $S_{0}$ branches against different types of perturbation: (a) in-between region, (b) outer region, (c) pillars, and (d) environment. In (a)–(c), the defect is mimicked by a $1 mm \times 1 mm$ inclusion with density being $ρ_{0} + Δ ρ$ and $Δ ρ / ρ_{0} \in {0, 0.1, 0.2, 0.3, 0.4}$ at particular locations. In (d) the environmental perturbation is introduced by varying the Young’s modulus of the entire structure as $E_{0} + Δ E$ with $Δ E / E_{0} \in {0, 0.01, 0.02, 0.03, 0.04}$ [53].
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Figure 4
Sensitivity analysis for local modes originated from multibranch BICs. (a) Simulated resonance frequencies of the local modes $A$ , $S_{I}$ and $S_{II}$ as a function of the in-between defect strength (left panel) and environmental perturbation (right panel). The strengths of the defect and environmental perturbation are controlled by the thickness, $t_{defect}$ , of an added block and the Young’s modulus, $E_{0} + Δ E$ , of the entire beam, respectively. (b) Simulated resonance frequencies of the bare beam as a function of defect strength. (c) Measured FRFs ( $| \dot{v} |$ ) of the pillared (upper panel) and bare (lower panel) beams. The solid (dashed) lines represent the intact (defective) case. (d) Measured vertical velocity fields of modes $A$ , $A^{d}$ , $S_{II}$ , $S_{II}^{d}$ , $C$ , and $C^{d}$ .
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